2015 AMC 12B Problem 5

The Tigers beat the Sharks

2

out of the first

3

times they played. They then played

N

more times, and the Sharks ended up winning at least

95\%

of all the games played. What is the minimum possible value for

N?

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Solution

The Sharks won

1

of the first

3

games. To reach

95\%

with the fewest extra games, they should win all

N

additional games, giving a win fraction

\dfrac{1 + N}{3 + N}.

Requiring

\dfrac{1 + N}{3 + N} \ge \dfrac{19}{20}

gives

20 + 20N \ge 57 + 19N,

N \ge 37.

Thus, the correct answer is B.

Tagged: percentage · inequality · extremal argument